Question: Rewrite as a simplified fraction. ${2.45\overline{4} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2454.4444...\\ 100x &= 245.4444...\end{align*}}$ Subtracting the two equations, we have: ${900x = 2209}$ ${x = \dfrac{2209}{900}} \text{or} {2 \dfrac{409}{900}}$